System Reliability Considerations

Preventive & Predictive Maintenance syahril@itenas.ac.id

1Reliability Systems Basic ConceptsSemester Genap 2014-2015In theory, if we were able to comprehend the exact physics and chemistry of a failure process, many internal failures of a component could be predicted with certainty. Ramdon to probabilistic2ReliabilityReliability is defined to be the probability that a component or system will perform a required function for a given period of time when used under stated operating conditions.Maintainability is defined to be the probability that a failed component or system will be restored or repaired to a specified condition within a period of time when maintenance is performed in accordance with prescribe procedure.Availability is defined as the probability that a component or system is performing its required function at a given point in time when used under stated operating conditions. 3Reliability cont.4The Bath Tub CurveBurn-InUseful LifeNote: Failure Rate is constantWear-OutTimeFailure Ratel5System Operational StatesUpDownA1A3A2tB1B2B3Up: System up and runningDown: System under repairSingkatan:BD = Break DownDT = Down TimeTBF = Time Between FailuresTTR = Time To RepairMDT = Mean Down TimeMTTR = Mean Time To RepairMTBF = Mean Time Between FailuresTBM = Time Between Maintenance

7Mean Time Between Failure (MTBF)MTBF is defined as the mean time between successive failures.MTBF =B1 + B2 + B33UpDownA1A3A2tB1B2B38Mean Time To Repair (MTTR)MTTF is defined as the mean time of the occurrence of the first failure after entering service.MTTR = A1 + A2 + A33UpDownA1A3A2tB1B2B39

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Out of service time (Down Time)12

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19The Concept of AvailabilityReliabilityMaintainabilityAvailability20ReliabilityReliability is the probability that a device or a system will operate without failure for a given period and under given operating conditions.R(t) = e-ltwhere l is failure rate21MaintainabilityMaintainability is the probability that a device or a system that has failed will be restored to operation effectiveness within a given time.M(t) = 1 - e-mtwhere m is repair (restoration) rate22AvailabilityAvailability is the proportion of the system Up-Time to the total time (Up + Down) over a long period.A =Up-TimeUp-Time + Down-Time23Capability: A measure of the ability of a product to satisfy given requirements (A measure of Quality - no time dependency)Availability: A measure of the ability of a product to complete a mission without excessive down time (Depends on Reliability and Maintainability)Dependability: A measure of the ability of a product to commence and complete a mission without failure (Depends on Reliability and Maintainability)24AvailabilityAvailability is defined as:A =Up-TimeUp-Time + Down-TimeAvailability is normally expressed in terms of MTBF and MTTR as:A =MTBFMTBF + MTTR25Reliability/Maintainability Measures(Failure Rate) l = 1 / MTBFR(t) = e-ltReliability R(t)Maintainability M(t)(Maintenance Rate) m = 1 / MTTRM(t) = 1 - e-mt26Failure Rate (l)Failure rate { l(t) } is a function of time, it is constant during the Useful Life of the device or system.If a piece of equipment has a failure rate l(t), its probability of survival from time 0 to t, or reliability R(t), is given by:

If the failure rate l(t) is constant, the expression reduces to:

A system has 4000 components with a failure rate of 0.02% per 1000 hours. Calculate and MTBF.

= (0.02 / 100) * (1 / 1000) * 4000 = 8 * 10-4 failures/hour

MTBF = 1 / (8 * 10-4 ) = 1250 hours 27A simple example27A first generation computer contains 10000 components each with = 0.5%/(1000 hours). What is the period of 99% reliability?

MTBF = t / (1 R(t)) = t / (1 0.99)t = MTBF * 0.01 = 0.01 / avWhere av is the average failure rateN = No. of components = 10000 = failure rate of a component = 0.5% / (1000 hours) = 0.005/1000 = 5 * 10-6 per hour

Therefore, av = N = 10000 * 5 * 10-6 = 5 * 10-2 per hour

Therefore, t = 0.01 / (5 * 10-2 ) = 12 minutes 28An example2829Reliability for different configurationsRRRRR1234NOverall reliability = Ro = R * R * R. R = RN

1. Series Configuration2. Parallel ConfigurationRRR12NRo = 1 (probability that all of the components fail)Ro = 1 (1 - R)N2930Reliability for different configurationsRRR12NOverall reliability = Ro = ?3. Hybrid ConfigurationRRR12M3031Reliability for different configurations4. Triple Modular Redundancy (TMR)RRR12MVotingOverall reliability = Ro = [3C2 * R2 * (1-R)] + [R3]3132Kuis : 2 ( Senin, 27 April 2015)Jika kita mempunyai dua pompa dimana spesifikasi setiap pompa adalah sebagai berikut :Pompa A : Q = 10 l/min H = 10 meter dan Reliability 0.9 atau 90%.Pompa B : Q = 20 l/min H = 8 meter dan reliability 0.85 atau 85%.Hitunglah reliability suatu sistem jika :ingin menaikkan air dengan Q = 30 l/min H = 7 mmenaikkan air dengan Q = 10 l/min dan H =16 m.